1. Field of the Invention
Profile control in the cross-machine direction of a paper machine involves a long dead time and a large time constant. As a result, this type of control takes a long time to stabilize for such events as a setpoint change, thus decreasing production efficiency. Another problem has been that a manipulated variable may overshoot after paper threading due to sheet break or after grade change. As a result, the manipulated variable takes a long time to settle, thereby also decreasing production efficiency.
The present invention relates to a process control method based on a finite settling-time response method. More particularly, the invention relates to a process control method and a process control apparatus preferred in controlling paper thickness profiles in the cross-machine direction of a paper machine.
2. Description of the Prior Art
FIG. 1 is a diagrammatic view showing the configuration of a system for controlling the paper thickness (CLP) profiles of a paper machine. In the figure, produced paper 51 is smoothed in its entirety and tuned in its thickness profile by a calender 53, and wound onto a reel 55. At this point, the thickness profile in the cross-machine direction of the produced paper 51 is measured by a CLP sensor 54 placed immediately before the reel 55. The CLP sensor 54 repeats a scan (round travel) across the paper 51 in the cross-machine direction at a speed of approximately 30 seconds per one-way travel, thus measuring the thickness profile of the paper 51.
A CLP measurement signal, which is the output of the CLP sensor 54, is input to a measurement computation unit 56, where the CLP measurement signal is converted to a digital signal at a maximum speed of approximately 60 Hz. Thus, a maximum of 1200 items of measured CLP data is obtained for each one-way travel. Such a collection of CLP measurement signals as acquired for each one-way travel is referred to as a CLP profile. The CLP profile is regarded as representing the cross-section of the paper 51 in the cross-machine direction, and used for the purpose of paper quality control. The CLP profile is considered especially important in the case of printing paper. For example, the quality of newspaper is stipulated such that a variable R, which is the deviation between the maximum and minimum variances in paper thickness, be kept at or below 1 xcexcm for an average paper thickness of 80 xcexcm.
The CLP profile is input to a control computation unit 57, where a controlled/manipulated variable for controlling a hot-air heater 52 is calculated. This controlled/manipulated variable is input through an interface panel 58 to the hot-air heater 52. The hot-air heater 52 blows air as hot as 40 to 400xc2x0 C. onto a calender 53 in order to change the diameter thereof by means of thermal expansion, thereby tuning the CLP profile. The heater is segmented into multiple zones at a spacing interval of 75 to 100 mm and the temperature setpoint of hot air is changed on a zone-by-zone basis, so that the diameter of the calender 53 in the cross-machine direction is varied and thereby the CLP profile is properly adjusted.
Now, zone-specific profiles used in CLP profile control will be explained with reference to FIG. 2. In the figure, a numeral 61 indicates paper, the width thereof being divided into N zones. A numeral 62 indicates the measurement points of paper thickness, which amount to Pt points. Since the number of measurement points is greater than the number of zones under normal conditions, a plurality of measurement points are allocated to each zone. FIG. 2 shows that five measurement points are allocated to each zone. Although dependent on the scale of a paper machine, N has a value from 50 to 100 in normal applications. Likewise, Pt has a value of 1200 at the largest, though this value depends on the length of frame used.
A CLP profile PRF(i) is the value obtained by subtracting the average of all the values of a CLP process variable RPV(i) from the value of the CLP process variable RPV(i) of each measurement point. Thus, the CLP profile PRF(j) is expressed as equation 1 below.
PRF(i)=RPV(i)xe2x88x92PVAVE(i=1, . . . ,Pt)xe2x80x83xe2x80x83(1)
where       PV    AVE    =            1      Pt        ⁢                  ∑                  j          -          1                Pt            ⁢              xe2x80x83            ⁢              RPV        ⁡                  (          i          )                    
A measurement point of a CLP profile positioned at the midpoint of an ith zone is referred to as the position-specific measurement point of that zone, and is represented as PC(i). The number of measurement points included in one zone is determined from the mechanical width of the hot-air heater and the spacing between the measurement points of paper thickness, and is represented as AP. By way of simplifying later discussion, AP is defined as an odd number. If any calculated value of AP happens to be even, 1 is added to the value to make it odd.
The zone-specific CLP profile of a zone i is defined as ZP(i), and expressed as equation 2 below.                               ZP          ⁡                      (            i            )                          =                              1            AP                    ⁢                                    ∑                              j                =                                  -                  BP                                            BP                        ⁢                          xe2x80x83                        ⁢                          PRF              ⁡                              (                                                      PC                    ⁡                                          (                      i                      )                                                        +                  j                                )                                                                        (        2        )            
where
i=1, . . . , N
PC(i)=Position-specific measurement point of ith zone   BP  =            AP      -      1        2  
CLP profile control refers to the type of control wherein a hot-air heater is controlled so that the CLP profile ZP(i) of each zone is flattened as much as possible.
Next, CLP profile control will be explained with reference to FIG. 3. The input to a controller 71 is a paper thickness deviation variable E(s), where a manipulated variable W(s) is calculated and output. The manipulated variable W(s) is input through a hold unit 72 to a process 73. The output of the process 73 is paper thickness C(s), which is fed back to the controller 71. G(s), H(s) and P(s) denote the transfer functions of the controller 71, hold unit 72 and process 73, respectively.
The transfer function P(s) of the process 73 can be approximated using a combination of a dead time and a first-order delay. Process measurement carried out in a certain paper machine using a step response method results in the dead time=5 min, time constant=8 min, and process gain=0.1 xcexcm/%.
In order to carry out such control as described above, a sampling PI control method has been used conventionally. More specifically, it has been the common practice of such control to calculate a change in the controlled/manipulated variable xcex94Wn(i) using equation 3 below.                               Δ          ⁢                      xe2x80x83                    ⁢                                    W              n                        ⁡                          (              i              )                                      =                              100            PB                    ⁢                      (                                          Δ                ⁢                                  xe2x80x83                                ⁢                                                      E                    n                                    ⁡                                      (                    i                    )                                                              +                                                TC                  TI                                xc3x97                                                      E                    n                                    ⁡                                      (                    i                    )                                                                        )                                              (        3        )            
where
xcex94Wn(i)=Change in the manipulated variable of ith zone (%)
xcex94En(i)=En(i)xe2x88x92Enxe2x88x921(i)
En(i)=Zone-specific CLP profile of ith zone
Enxe2x88x921(i)=Zone-specific CLP profile of ith zone measured one control period earlier
TC=Control period, i.e., time required for a one-way travel of scan (sec)
PB=Proportional band (%)
TI=Integral time (sec)
FIG. 4 shows the result of simulating the response of the process to a steplike disturbance, using the Chien-Hrones-Reswick method which is a typical method for determining a PI gain from a step response. The horizontal axis represents time in units of a control period (number of scans). Note that in this simulation, we defined the dead time L as 300 sec, time constant T as 480 sec, proportional band as 167xc3x97L/T, and integral time TI as T. This combination of settings minimizes the response to 20% overshoot. In FIG. 4, a numeral 81 indicates a control deviation variable and a numeral 82 denotes a change in the manipulated variable. As is evident from the figure, the process requires as many as 25 scans (750 sec) for 80% response and as many as 45 scans (1350 sec) for 90% response. This means that the process has extremely poor response.
The present invention is intended to provide a highly responsive method of control based on a finite settling-time response method. More specifically, the invention provides a method for controlling a process by inputting a deviation between setpoint and process variables to a controller to calculate a controlled/manipulated variable, and then inputting the controlled/manipulated variable to the process, wherein conditions for the process variable to settle within a finite length of time are determined from the final-value theorem, the transfer function of the controller is derived from the conditions, and the value of or change in the controlled/manipulated variable with which to control the process is calculated using the transfer function. As a result, it is possible to allow even a process with a long dead time and a large time constant to settle within a short length of time, thereby increasing the efficiency of production.